Total Internal Reflection

Snell's law governs every ray crossing a boundary: n1 sin(theta1) = n2 sin(theta2). When light moves from a slower medium (higher n) into a faster one (lower n), like glass into air, the refracted ray bends away from the normal. As you increase the angle of incidence, the refracted ray swings closer and closer to the surface itself. At one specific angle, the critical angle, the refracted ray lies flat along the boundary at a full 90 degrees. Push past that angle and there is no possible refraction angle that satisfies Snell's law, so all the light reflects back inside. That is total internal reflection: not partial, not dim, total.

The critical angle depends only on the two indices: sin(theta_c) = n2/n1, or when the second medium is air (n close to 1), sin(theta_c) = 1/n. This is why looking up at a pool surface from underwater at a shallow angle shows a mirror-like ceiling: past the critical angle, the surface stops letting light out and instead reflects your view of the pool bottom back at you.

This effect only works going from high index to low index. Light entering a denser medium always bends toward the normal and always finds a valid refraction angle, no matter how steep the incidence, so there is no critical angle in that direction. Fiber optic cables exploit the one-way nature of this rule: light enters a glass core surrounded by a lower-index cladding, strikes the core-cladding boundary beyond the critical angle every time, and reflects down the fiber for kilometers with almost no loss, bouncing wall to wall instead of leaking out.